This invention relates to a multidomain method for evaluating the formation of thin films on semiconductor substrates using optical methods, and an apparatus embodying the method.
Optical methods for measuring samples are generally known, in particular, for semiconductor fabrication involving the formation of a stack of thin film layers on a semiconductor substrate. Such methods are considered essential for the efficient operation of modern fabrication facilities. Optical methods are desirable because they are non-destructive and the resultant optical data can be used to derive information regarding layer parameters, such as thickness, refractive index, extinction coefficient, dispersion and scattering, for multiple layers of a thin film stack.
One preferred approach includes the use of the OPTIPROBE detector manufactured and sold by Therma-Wave, Inc. of Fremont, Calif., assignee herein, and described in part in one or more of the following U.S. Pat. Nos.: 4,999,014; 5,042,951; 5,181,080; 5,412,473; and PCT publication WO 99/02970, each of which is incorporated herein by reference in its entirety.
Conventional optical processing technology typically relies upon using a non-linear least squares algorithm to fit the measured data to a set of data points with a solution representing specific parameters of a thin film stack.
Improvements in optical technologies can provide an ever-increasing number of measured data points, which in turn provide the opportunity for deriving layer parameters on more complicated film stacks. However, this opportunity also presents a more complex optimization problem for developing solutions based on the observed data, and conventional processing techniques (such as least squares algorithms) are inadequate to handle the increased complexity.
Genetic Algorithms (GA""s) have been applied to the problem of adaptive function optimization. A basic theoretical framework for GA""s is described in Holland, Adaptation in Natural and Artificial Systems (1975). The terminology used by Holland is borrowed from genetics. Thus, in the computer analog, a GA is a method for defining a xe2x80x9cpopulationxe2x80x9d of solutions to a selected problem, then evolving new populations by using probabilistic genetic operations to act on xe2x80x9cindividualxe2x80x9d members of the population, i.e. individual solutions. Each individual in the population has a plurality of xe2x80x9cgenes,xe2x80x9d which are each representative of some real parameter of interest. For example, if there are x data parameters of interest, each individual would have x genes, and populations of individuals having x genes would be propagated by a GA.
The use of GA""s for function optimization is generally described in U.S. Pat. Nos. 5,222,192 and 5,255,345, both to Schaefer. Further, U.S. Pat. No. 5,394,509 to Winston generally describes the application of GA""s to search for improved results from a manufacturing process. Also, there has recently been much interest in the use of GA""s in the design of various types of optical filters. See Eisenhammer, et al., Optimization of Interference Filters with Genetic Algorithms Applied to Silver-Based Heat Mirrors, Applied Optics, Vol. 32 at pp. 6310-15 (1993); and Bxc3xa4ck and Schxc3xctz, Evolution Strategies for Mixed-Integer Optimization of Optical Multilayer Systems, Proceedings of the Fourth Annual Conference on Evolutionary Programming at pp. 33-51 (1995).
More recently, GA""s have been applied to the problem of evaluating thin films on semiconductor wafers. U.S. Pat. No. 5,864,633, hereby incorporated by reference in its entirety, describes the application of GA""s to the problem of evaluating the characteristics of thin film layers with an optical inspection device. The present invention is directed to an improvement on the method disclosed in U.S. Pat. No. 5,864,633 involving a multidomain optimization technique.
The technique described in U.S. Pat. No. 5,864,633 relates to an invention useful for converting optical measurements at a point on a semiconductor wafer into a description of the thin films beneath that point on the wafer. This application describes a modification of the GA technique described in U.S. Pat. No. 5,864,633 in order to improve either the evaluation of wafer measurements at multiple points on a wafer or the evaluation of (possibly multiple) measurements of multiple wafers.
The present invention provides a suitable multidomain optimization technique for doing this wherein two or more populations of genotypes are used. In general one evolving genotype population is employed for each of the individual measurement points on the wafer. Flags are used to divide the genes of the genotypes into two categories or classes: local and global. Local genes represent parameters that are only associated with one domain whereas global genes represent parameters associated with more than one domain. More than one category of global gene may be employed.
By subdividing the genes into global and local categories and employing a migration step that allows genotypes to move among two or more domains, the present invention improves the evaluation of the sample compared with the method taught in U.S. Pat. No. 5,864,633. This is so because the present invention allows the optimization process to reflect the possibility that some parameters may be constant or nearly constant across multiple domains whereas others may not be.
Multiple generations of the genotypes in each domain are evolved until an acceptable solution is obtained. Using conventional Fresnel equations, a processor derives theoretical data from the theoretical parameters defining each of the genotypes. The derived theoretical data for a given genotype are compared with the actual measured data in accordance with a fitness function. The fitness function provides a measure of how close the derived theoretical data are to the measured data. Individual genotypes are then selected based on this fitness comparison. Genetic operations are performed on the selected genotypes to produce new genotypes. In addition to crossover, direct reproduction, and mutation operations, a migration step is performed that allows genotypes to migrate among two or more domains.